Wicket-keeper Geraint Jones backed his bowlers with a pair of splendid catches before India reached 153-5 at lunch on the third day in reply to England's first-innings total of 400.
Wicket-keeper Mahendra Dhoni was unbeaten on 32 at the interval with lower-order batsman Irfan Pathan on seven. India need 48 more runs to avoid the follow-on.
The day began impressively for England, seeking a win here to square the series after losing the second Test by nine wickets at Mohali. The opening match at Nagpur ended in a draw.
Stand-in captain Flintoff struck in his opening over when he removed Yuvraj Singh (37) on Monday after the hosts had added just five runs to their overnight total of 89-3.
Left-handed Yuvraj was out to a rash shot as he attempted to cut a delivery going outside the off-stump, only to see Jones diving in front of first slip to bring off a low catch.
India suffered a major setback when they lost well-set captain Rahul Dravid (52), caught down the leg-side by a diving Jones off Anderson. He fell shortly after completing his 42nd Test half-century.
Anderson, playing his first Test in more than a year, deserved more than one wicket in his inspiring opening spell.
He was the unlucky bowler when Monty Panesar dropped Dhoni at mid-off and then substitute Matt Prior let off Dravid at gully in the space of three deliveries. Dhoni was then on 23 and Dravid on 52.
The Indian batsmen had a torrid time in the morning session, with swing bowler Matthew Hoggard and Flintoff posing problems with pace and bounce in their opening spells.
Dhoni got a nasty blow on the helmet while ducking into a Flintoff bouncer, but recovered quickly to pull the next ball for four. He continued playing shots under pressure, hammering Flintoff for another four in the next over.
Anderson and Hoggard have so far grabbed two wickets apiece and Flintoff one.